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The word space in space architecture is referring to the outer space definition, which is from English outer and space. Outer can be defined as "situated on or toward the outside; external; exterior" and originated around 1350–1400 in Middle English. [4] Space is "an area, extent, expanse, lapse of time," the aphetic of Old French espace ...
The 5-sphere, or hypersphere in six dimensions, is the five-dimensional surface equidistant from a point. It has symbol S 5, and the equation for the 5-sphere, radius r, centre the origin is = {: ‖ ‖ =}. The volume of six-dimensional space bounded by this 5-sphere is
The Gromov–Hausdorff space is path-connected, complete, and separable. [5] It is also geodesic, i.e., any two of its points are the endpoints of a minimizing geodesic. [6] [7] In the global sense, the Gromov–Hausdorff space is totally heterogeneous, i.e., its isometry group is trivial, [8] but locally there are many nontrivial isometries.
An important uniform 5-polytope is the 5-demicube, h{4,3,3,3} has half the vertices of the 5-cube (16), bounded by alternating 5-cell and 16-cell hypercells. The expanded or stericated 5-simplex is the vertex figure of the A 5 lattice, . It and has a doubled symmetry from its symmetric Coxeter diagram.
The Kruskal–Szekeres coordinates also apply to space-time around a spherical object, but in that case do not give a description of space-time inside the radius of the object. Space-time in a region where a star is collapsing into a black hole is approximated by the Kruskal–Szekeres coordinates (or by the Schwarzschild coordinates).
A sphere formed using the Chebyshev distance as a metric is a cube with each face perpendicular to one of the coordinate axes, but a sphere formed using Manhattan distance is an octahedron: these are dual polyhedra, but among cubes, only the square (and 1-dimensional line segment) are self-dual polytopes.
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Unlike a flat-space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime. The Nariai limit has no singularities , the cosmological and black hole horizons have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch.